EIN 4354 Fall 03Homework 3
Due 9/22/03 (Section 2613) and 9/23/03 (Section 2612)
Problem 1
A bank recently announced an “instant cash” plan for holders of its bank credit cards. A cardholder may receive cash from the bank up to a pre-set limit. There is a special charge of 4% made at the time the “instant cash” is sent to the cardholders. The debt may be repaid in monthly installments. Each month the bank charges 1½% on the unpaid balance. The monthly payment, including interest, may be as little as $10. Thus, for $150 of “instant cash,” an initial charge of $6 is made and added to the balance due. Assume the cardholder makes a monthly payment of $10 (this includes both principal and interest) to receive the “instant cash.” How many months are required to repay the debt? If your answer includes a fraction of a month, round up to the next month.
Problem 2
The football coach at a Midwest university was given a five-year employment contract which paid $225,000 at the beginning of the first year, and increases at an 8% rate in each subsequent year. At the end of the first year’s football season, the alumni demanded that he be fired. The alumni agreed to buy the coach’s remaining four years on the contract by paying him the equivalent present sum, computed using a 12% interest rate. How much will the coach receive?
Problem 3
What is the future worth of a series of equal deposits of $2,000 for 10 years in a savings account that earns 9%, annual interest, if
a)All the deposits were made at the end of each year?
b)All the deposits were made at the beginning of each year?
Problem 4
The two cash flow transactions shown in the cash flow diagram are said to be equivalent at 10% interest, compounded annually. Find the unknown X value which satisfies the equivalence.
Problem 5
In computing either the equivalent present worth (P) or future worth (F) for the cash flow, at i = 10%, identify all the correct equations from the list below to compute them.
(1)P = R (P/A, 10%, 6)
(2)P = R + R (P/A, 10%, 5)
(3)P = R (P/F, 10%, 5) + R (P/A, 10%, 5)
(4)F = R (F/A, 10%, 5) + R (F/P, 10%, 5)
(5)F = R + R (F/A, 10%, 5)
(6)F = R (F/A, 10%, 6)
(7)F = R (F/A, 10%, 6) – R
Problem 6
How many years will it take an investment to triple itself if the interest rate is 9%, compounded annually?
Problem 7
What is the equal payment series for 10 years that is equivalent to a payment series of $12,000 at the end of the first year, decreasing by $1000 each year over 10 years? Interest is 8%, compounded annually.
Problem 8
War Eagle Financial Sources, which makes small loans to college students, offers to lend $400. The borrower is required to pay $26.61 at the end of each week for 16 weeks. Find the interest rate per week. What is the nominal interest rate per year? What is the effective interest rate per year?